CaptainEd

I don't feel strong enough yet, but the Den is strong...

Wow! This is a lot of cases, and I'll probably miss some in my exhaustive enumeration. Are you suggesting that we might be able to REASON this out, rather than list many dozens of cases? Thanks for the puzzle, by the way

And Nice Puzzle to you, again and forever!

I see k-man's point: if the randomizer is really indifferent to whether his/her answer is true or false, then why would he/she be "forced by the paradox to evaluate the truth value..." Why not just flip the coin? There's no requirement that the randomizer actually knows the truth or falsity of his/her answer. I'm reminded of an old Superboy episode (yes, way old...) where a special kind of Kryptonite made Superboy into Pinocchio--whenever he lied, his nose grew longer. Superboy used this to figure out where the bad guys were hiding, by uttering the words "the bad guys are North of Main Street". When his nose grew longer, he knew that the bad guys were actually South of Main Street. This was an odd theory of "lying"--saying something that doesn't happen to be true, even though you don't know it. But our randomizer could be this way. (Actually, I generally interpret one of these "randomizers" as being more like Maxwell's daemon--he does something pathological, whatever will best thwart your intended theory) Now Bonanova's answer has come in. OK, I can bear that interpretation--the randomizer makes an explicit choice between lying and telling the truth. Having made that choice, he/she figures out what IS the truth, and then tells the truth or lies. Humph. Yes, having a unanimous crowd is very pleasing!

TSLF, I'm glad you responded about the 5 and 7. It made me realize that I didn't fully understand my naive belief that "complementation" should preserve balance. As your example points out, the solution for 7 is NOT the complement of a solution for 5. So I wonder whether, for a larger centrifuge, of size N, the presence of a solution for M samples guarantees the existence of a solution for N-M samples.

Araver, I guess that means we don't have it right. So I've got a question for you

Good solve, CaptainEd. Nice and compact solution =) Thank you both so much!

Rather easy when you put it that way...

I think the same words would apply equally well if the die had sides reading 0,1,1,1, rather than 0,1,2,3, yet I feel the probability of going bust should be different. Perhaps that's the trick that I'm falling for.

Oh, woops! Uh, no...especially on a day when I can't even code a spoiler

Phil, how does your progression incorporate the population increase?

Yes, now you guys have made it pretty clear

Right. The problem properly sated is to be the first to draw three numbers that total 15. Sorry to be dense. Is this true: I win if I am the first to have drawn M chips (M>=3), exactly 3 of which total 15?

I see, I was solving a different problem anyway, thinking that we were driving the combined total to 15. Let's see if I've got it right now. Each person is trying to achieve his/her own total of 15. And each person has to achieve his/her sum using three chips.

I'm assuming that the chips are taken out of circulation once selected. , my opponent chooses N (not equal to 5), and I choose 10-N

Yes, but that's physics. My father was a nuclear physicist in the 50's, in the slide rule era. When I was in high school, he explained to me a couple of important principles of applied mathematics: * For large enough N, anything = 1 * For really large enough N, anything = 0 As a corollary, he pointed out (for a different problem than this one), that "2 is one of the larger numbers that is equal to 1". But that's physics...

Nothing wrong with the wording. You didn't give away the trick, but you didn't hide it. It's just that many of us (*palm*) weren't open minded. I, too, couldn't get anything but all zeroes. Good puzzle! Thanks again for the education!

Prime, I agree--dropping (2), as you and Rainman did, was more interesting. I was excited to see the Rainman solution, and I then admired your transformation so that people could tell where the colors are even without colored chairs.